Method for estimating the position of a rotor of a synchronous electrical machine

ABSTRACT

A method for estimating the position of a rotor of a synchronous electrical machine, includes a rotor and a stator coupled to an inverted synchronous electrical machine via a rectifier comprising the following steps: measurement of a current i abc  circulating in the stator of the synchronous electrical machine; determination of two signals in quadrature i α ; i β  according to a stationary reference frame from the current i abc  and isolation of two filtered signals i αh ; i βh  from the two signals in quadrature i α ; i β ; demodulation of the two filtered signals i αh ; i βh  in order to obtain two demodulated signals i αobs , i βobs , obtaining of an estimated position {circumflex over (θ)} of the rotor from the two demodulated signals i αobs , i βobs .

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to foreign French patent applicationNo. FR 2011885, filed on Nov. 19, 2020, the disclosure of which isincorporated by reference in its entirety.

FIELD OF THE INVENTION

The invention relates to the control of rotating electrical machines.More particularly, the invention relates to a method that makes itpossible to estimate the position of a rotor of a rotating electricalmachine. The invention is particularly suited to estimating the positionof a rotor of a rotating electrical machine operating at low speed orwhen stopped. The invention is of particular use in the field ofrotating machines operating without mechanical sensors for sensing theposition of the rotor as in the field of aeronautics where the currenttrend is to limit the embedded weight in aeroplanes.

BACKGROUND

The rotating electrical machines of brushless synchronous machine typeand with multiple stages are used on a large scale in the aeronauticalfield. For example, they can be used in order to provide a strong torquein the start-up phases of the engines with which they are associated.

These new motorisation systems require the knowledge, at any moment, ofthe position of the rotor for efficient commands to be generated. Now,according to the architecture of the systems that use mechanicalsensors, the location of these machines in proximity to the enginerepresents an extremely severe constraint demanding mechanical sensorsoperating in an environment raised to very high temperature. Thus, theuse of mechanical sensors under these extreme constraints becomes aconstraint for the design.

Moreover, depending on the types of synchronous machines used, themechanical integration of the rotor position sensor on the machine canbe a real problem. In fact, the compactness of the current synchronousmachines desired by aircraft manufacturers curbs the insertion of suchsensors.

This is all the more true since dispensing with a mechanical positionsensor allows for a weight saving linked to the elimination of thesensor and to the reduction of the number of cables between theelectronic used in startup and the rotating electrical machine.

At very low speed and when stopped, techniques can be used to estimatethe position of a synchronous electrical machine. Among thesetechniques, the injection of signals at high frequency into the statoror at the rotor makes it possible to induce a current response whichdepends on the real position of the rotor.

The methods involving the injection of signals at high frequency intothe stator are usually employed for the estimation of the position ofthe rotor but they have drawbacks:

-   the injection of the signals at high frequency can produce a    disturbance in the electromagnetic torque of the rotating electrical    machine, without the amplitude of the useful current containing the    position information being sufficient for the processing of that    datum.-   The harmonics produced at high frequency do not contain information    on the real polarity of the rotor. A special polarity identification    sequence is thus necessary.

The injection of signals at high frequency on the stator thereforepresents drawbacks in the case of the estimation of the position of therotor.

Conversely, the injection of signals at high frequency on the rotor canbe envisaged because it allows for an estimation of the position from acurrent induced in the stator which contains the information on theposition without uncertainty concerning the polarity. Furthermore, theset of harmonics induced on the stator has a low amplitude for the samequantity of signals injected compared to any injection method on thestator, which means less significant disturbances. However, someelements, such as, for example, the rectifier bridges, make it difficultto inject a signal directly on the rotor.

The documents CN 106959430 A and CN 107134962 A thus propose a methodfor estimating the position of the rotor.

SUMMARY OF THE INVENTION

The invention aims to wholly or partly overcome the problems cited aboveby proposing a method for estimating the position of a rotor from thestator current of a rotating electrical machine via harmonics that existnaturally in the stator current of the rotating electrical machine. Thisestimation is therefore obtained without greatly modifying the existingsystem and without the injection of additional signals either on therotor, or on the stator, which could introduce torque disturbances. Ananalysis of the stator currents makes it possible to estimate theposition directly without uncertainty concerning the polarity andwithout adding additional measurements.

Thus, the position estimation is made robust in the context of a moreelectrical aeroplane. The invention makes it possible to enhance thereliability of the overall system, which represents a major benefit, byway of example, in the field of aeronautics where the avionics systemsneed to be as reliable as possible.

To this end, the subject of the invention is a method for estimating theposition of a rotor of a synchronous electrical machine, comprising arotor and a stator coupled to an inverted synchronous electrical machinevia a rectifier comprising the following steps:

-   a) measurement of a current i_(abc) circulating in the stator of the    synchronous electrical machine;-   b) determination of two signals in quadrature i_(α); i_(β) according    to a stationary reference frame from the current i_(abc) and    isolation of two filtered signals i_(αh); i_(βh) from the two    signals in quadrature i_(α); i_(β);-   c) demodulation of the two filtered signals i_(αh); i_(βh) in order    to obtain two demodulated signals i_(αobs), i_(βobs);-   d) obtaining of an estimated position B of the rotor from the two    demodulated signals i_(αobs), i_(βobs).

According to an aspect of the invention, the estimated position{circumflex over (θ)} estimated in the step d is made according to thefollowing mathematical expression:

$\overset{\hat{}}{\theta} = {{atan}\left( \frac{i_{\beta\;{obs}}}{i_{\alpha\;{obs}}} \right)}$

According to an aspect of the invention, the estimated position{circumflex over (θ)} estimated in the step d is made using an observer.

According to an aspect of the invention, the two filtered signalsi_(αh); i_(βh) have a frequency combining an operating frequency of theinverted synchronous electrical machine and a frequency of thesynchronous electrical machine.

According to an aspect of the invention, the isolation of the twofiltered signals i_(αh); i_(βh) from the two signals in quadraturei_(α); i_(β) is performed using a bandpass filter or a high-pass filter.

According to an aspect of the invention, the step of demodulation of thetwo filtered signals i_(αh); i_(βh) uses a measurement of a currenti_(ex) of the stator of the inverted synchronous electrical machine.

According to an aspect of the invention, the estimation method comprisesa step of filtering of the two demodulated signals i_(αobs), i_(βobs)between the step c and the step d, the filtering step being performedusing a bandpass filter or an extended Kalman filter.

According to an aspect of the invention, the estimation method comprisesa step of estimation of the speed {circumflex over ({dot over (θ)})} ofthe rotor of the synchronous electrical machine from the estimatedposition {circumflex over (θ)} of the rotor of the synchronouselectrical machine.

According to an aspect of the invention, the estimation method comprisesa step of correction of the estimated position {circumflex over (θ)}with the following mathematical formula:

{circumflex over (θ)}_(corr)={circumflex over (θ)}+{circumflex over(ϕ)}_(corr)

in which {circumflex over (ϕ)}_(corr) is a correction of the delays onthe estimation of the position and {circumflex over (θ)}_(corr) is acorrected position of the rotor of the synchronous electrical machine.

According to an aspect of the invention, the correction of the delays{circumflex over (ϕ)}_(corr) is the sum of a phase-shift correction ofthe filters used {circumflex over (ϕ)}_(F) in the estimation method andof a phase-shift correction dependent on the electromagneticcharacteristics of the synchronous electrical machine {circumflex over(ϕ)}_(LC).

According to an aspect of the invention, the estimation method can berepeated periodically, and the demodulation step is preceded by a stepof evaluation of a phase {circumflex over (ϕ)} of a carrier from thefiltered signals i_(α) _(h) ; i_(β) _(h) , of an angular frequencyω_(ex) of the inverted synchronous electrical machine and of theestimated position {circumflex over (θ)} in a preceding iteration of theestimation method, the carrier being obtained at the rotor of theinverted synchronous electrical machine.

Similarly, the subject of the invention is a device for estimating theposition of a rotor of a synchronous electrical machine coupled to aninverted synchronous electrical machine via a rectifier for operationwhen stopped or at low speed comprising:

-   a module for measuring a current i_(abc) circulating in the stator    of the synchronous electrical machine;-   a module for determining and isolating harmonics of two filtered    signals i_(αh); i_(βh) from the current i_(abc);-   a module for demodulating the two filtered signals i_(αh); i_(βh)    from a measurement of the current i_(ex) of the stator of the    inverted synchronous electrical machine or of a carrier of angular    frequency co of the inverted synchronous electrical machine in order    to obtain two demodulated signals i_(αobs), i_(βobs);-   an obtaining module configured to determine an estimated position    {circumflex over (θ)} of the rotor of the synchronous electrical    machine from the two demodulated signals i_(αobs), i_(βobs).

According to an aspect of the invention, an electrical machine comprisesan inverted electrical machine and at least one synchronous electricalmachine equipped with the estimation device.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood and other advantages will becomeapparent on reading the detailed description of an embodiment given byway of example, the description being illustrated by the attacheddrawing in which:

FIG. 1A schematically illustrates a method for estimating the positionof a rotor of a rotating electrical machine according to the invention.

FIG. 1B represents the last two stages of a rotating electrical machinewith multiple stages comprising a device for estimating the position ofthe rotor at low speed and when stopped.

FIG. 1C schematically illustrates the method for estimating the positionof a rotor of a rotating electrical machine according to a variant.

FIG. 2A schematically illustrates the estimation method in a morecomprehensive version, that is to say comprising additional steps ofprocessing of the signal for the estimation of the position of the rotorof a rotating electrical machine according to the invention.

FIG. 2B represents the last two stages of a rotating electrical machinewith multiple stages comprising a device for estimating the position ofthe rotor in a more comprehensive version, that is to say one comprisingother signal processing modules concerning the position of the rotor ofa rotating electrical machine according to the invention.

FIG. 2C schematically illustrates a step of evaluation 16 of the phaseof a carrier schematically represented in FIG. 2B.

FIG. 3 represents the equivalent reference frames of representation of acurrent i_(abc) by using the Concordia or Clarke transformations to astationary reference frame (α,β) allowing conservation of the power andof the amplitude respectively.

FIG. 4 is a harmonics spectrum of a signal i_(αh); i_(βh) of the mainmachine when the rotor current contains a harmonic of high frequency,notably f_(ex) in this application.

In the interests of clarity, the same elements will bear the samereferences in the different figures.

DETAILED DESCRIPTION

The term “main machine” designates any synchronous rotating electricalmachine, provided or not provided with one or more dampers. The term“exciter” designates any synchronous rotating electrical machine that isinverted with respect to the main machine. The exciter is connected tothe main machine by a rotating diode bridge also called currentrectifier that makes it possible to obtain a direct current from analternating current.

FIG. 1A schematically represents a method for estimating 1 an estimatedposition {circumflex over (θ)} of a rotor 31 of a main machine 3 in thelast two stages of a rotating electrical machine 2 composed of the mainmachine 3, an exciter 4 and an estimation device 100, represented inFIG. 1B, for estimating the position of a rotor of a synchronouselectrical machine.

The method for estimating 1 the position of a rotor of a main machinemeasures a current i_(abc) circulating on the stator 32 and a currenti_(ex) originating from an exciter 4 measured on a stator 42 of theexciter 4 which is a single-phase alternating current of constantfrequency f_(ex). The method for estimating 1 the position of a rotor ofa synchronous electrical machine comprises the following four steps:

-   a step of measurement 11 of a current i_(abc) circulating in the    stator 32 of the main machine 3 and, possibly, of a current i_(ex)    originating from the exciter 4 at the stator 42. The current i_(abc)    is a three-phase current i_(a), i_(b), i_(c) of the same frequency    f_(e) of the main machine 3 phase-shifted by 120 degrees. The    measurement step 11 also makes it possible to eliminate the    measurement noise at the same time as the current i_(abc).    Furthermore, it is possible to envisage, according to certain    conditions, measuring only two phases of the stator current and    deducing the third therefrom according to the phase law of    three-phase currents:

i _(a) +i _(b) +i _(c)=0

a step of determining and of isolation of harmonics 12 that makes itpossible to obtain two filtered signals i_(αh); i_(βh) from the currenti_(abc). The determination and isolation step 12 comprises steps ofdetermination 12A of two signals in quadrature i_(α); i_(β) from thecurrent i_(abc) of the stator 32 according to a stationary referenceframe and of isolation 12B of the two signals in quadrature i_(α); i_(β)in order to obtain two filtered signals i_(αh); i_(β). Morespecifically, the current i_(abc) is transformed into a stationaryreference frame (α,β) that allows a three-phase system to be modelled.Preferentially, the current i_(abc) is transformed into the referenceframe (α,β) by a Clarke transformation for the purposes of powerconservation and can be transformed into the reference frame (α,β) by aConcordia transformation for the purpose of amplitude conservation.Advantageously, the polyphase machines, hexaphase for example, haveequivalent transformations to a stationary reference frame, which makeit possible to keep the invention applicable. The two signals arefiltered in the isolation step 12B in order to isolate only theharmonics of interest. The two filtered signals obtained, whichrepresent the image of the harmonics of interest for the person skilledin the art, are thus named i_(αh); i_(βh). As an example, the isolation12B of the two filtered signals i_(αh); i_(βh) from the two signals inquadrature i_(α); i_(β) can be performed using a bandpass filter orhigh-pass filter. Nevertheless, any means whose function is to eliminatethe signals at low frequency in favour of the high-frequency signalsand/or that makes it possible to eliminate all the disturbancesoriginating from the environment of the main machine 3 can be taken intoconsideration in the isolation 12B of the two filtered signals i_(αh);i_(βh). As an example, the use of a frequency transformation, such asthe Park transformation, and a digital filtering in order to isolate theharmonics at a frequency which does not change in time despite therotating of the machine, as represented in FIG. 1C, offers this functionof elimination of the signals at low frequency in favour of thehigh-frequency signals.

The two filtered signals i_(αh); i_(βh) are advantageously signals orharmonics whose frequency combines the operating frequency f_(ex) of theexciter 4 or of one of its multiples and the frequency f_(e) of the mainmachine 3 as FIG. 4 shows. Preferentially, the two filtered signalsi_(αh); i_(βh) have a frequency of the form f_(e−) ⁺2*f_(ex).Nevertheless, it is possible to envisage using filtered signals with adifferentiated form such as f_(e−) ⁺4*f_(ex) or even f_(e−) ⁺6*f_(ex).The two filtered signals i_(αh); i_(βh) then form a pair of harmonicscentred around the fundamental component. Thus, the two filtered signalsi_(αh); i_(βh) have a frequency which can be defined according to thefollowing formula:

f_(e−) ⁺n*f_(ex)

in which n represents an even relative integer number, that is to saythe number of pairs of poles on the stator.

A step of demodulation 13 of the two filtered signals i_(αh); i_(βh) inorder to obtain two demodulated signals i_(αobs), i_(βobs). In order todemodulate the two filtered signals i_(αh); i_(βh), the demodulationstep 13 uses, for example, a measurement of the current of the exciteri_(ex) which can be determined on the stator 42 of the exciter 4 in themeasurement step 11 or even an estimation of a carrier of angularfrequency ω_(ex) of the exciter 4 as illustrated in FIGS. 2A and 2B.

More specifically, the two filtered signals i_(αh); i_(βh) having anamplitude A, can be written in the form:

$\begin{matrix}{\begin{bmatrix}i_{\alpha h} \\i_{\beta h}\end{bmatrix} \approx {{A\begin{bmatrix}{\cos(\theta)} \\{\sin(\theta)}\end{bmatrix}}{\sin\left( {{2\omega_{ex}t} + \phi} \right)}}} & (1)\end{matrix}$

With θ the real position of the rotor 31 of the main machine 3 andω_(ex)=2πf_(ex) the angular frequency of the current of the exciter 4.With ϕ, the phase of the harmonic of the current induced on the rotor31, a harmonic that will be called carrier.

The observed demodulation consists in eliminating the termsin(2ω_(ex)t+ϕ) from the Equation (1).

One way of producing the demodulation consists in multiplying theEquation (1) by a signal which emulates the signal of the carrier. Thissignal must have the frequency and the phase of the carrier. Now, inknowing that the carrier cannot be measured, the signal can bereconstructed from the measurement of the current of the exciter i_(ex).An example of simple processing of the excitation current forreconstruction of the carrier can be:

${\sin\left( {{2\omega_{ex}t} + \overset{\hat{}}{\phi}} \right)} \approx {\frac{4{i_{ex}}}{I_{ex}} - 1}$

With I_(ex) the “peak to peak” amplitude of the excitation current and{circumflex over (ϕ)} the approximate phase of the carrier thusobtained.

In order to allow the person skilled in the art to more accuratelycontrol the phase ϕ of the carrier, other solutions can be envisaged,such as, for example, the use of an observer that takes account of thedynamics of a rectifier 5, represented in FIG. 1B, making it possible toobtain a direct current from an alternating current and of the circuitof the rotor 31 of the main machine 3, represented in FIG. 1B.

Another filtering of the two demodulated signals i_(αobs), i_(βobs),representing the two filtered signals i_(αh); i_(βh) after having beendemodulated, called H_(F)(s) is then applied in order to obtain only thelow-frequency information. The following formula is then obtained forthe two demodulated signals i_(αobs), i_(βobs):

$\begin{matrix}{\begin{bmatrix}i_{\alpha\;{obs}} \\i_{\beta\;{obs}}\end{bmatrix} = {{H_{F}(s)}\left( {{2\ \begin{bmatrix}i_{\alpha h} \\i_{\beta h}\end{bmatrix}}{\sin\left( {{2\omega_{ex}t} + \overset{\hat{}}{\phi}} \right)}} \right)}} & (2)\end{matrix}$

The signal to be filtered in the Equation (2) can then be developedusing the formula (1) as follows:

$\begin{matrix}{{\begin{bmatrix}i_{\alpha h} \\i_{\beta h}\end{bmatrix}{\sin\left( {{2\omega_{ex}t} + \overset{\hat{}}{\phi}} \right)}} = {{A\begin{bmatrix}{\cos(\theta)} \\{\sin(\theta)}\end{bmatrix}}{\sin\left( {{2\omega_{ex}t} + \phi} \right)}{\sin\left( {{2\omega_{ex}t} + \overset{\hat{}}{\phi}} \right)}}} & (3)\end{matrix}$

Thus, through the trigonometrical formulae, it is possible to reveal thelow-frequency component which is obtained following the filtering in theEquation (2):

$\begin{matrix}{{\begin{bmatrix}i_{\alpha h} \\i_{\beta h}\end{bmatrix}{\sin\left( {{2\omega_{ex}t} + \overset{\hat{}}{\phi}} \right)}} = {{\frac{A}{2}\begin{bmatrix}{\cos(\theta)} \\{\sin(\theta)}\end{bmatrix}}\left( {{\sin\left( {\phi - \overset{\hat{}}{\phi}} \right)} - {\cos\left( {{4\omega_{ex}t} + \phi + \overset{\hat{}}{\phi}} \right)}} \right)}} & (4)\end{matrix}$

Now, as stated previously, with the approximate phase {circumflex over(ϕ)} making it possible theoretically to compensate the phase ϕ presentin the estimated carrier, the sine of their difference is ideallyequivalent to sin(ϕ−{circumflex over (ϕ)})≈sin(0)=1.

Thus, the formula (4) then becomes:

$\begin{matrix}{{\begin{bmatrix}i_{\alpha h} \\i_{\beta h}\end{bmatrix}{\sin\left( {{2\omega_{ex}t} + \overset{\hat{}}{\phi}} \right)}} = {{\frac{A}{2}\begin{bmatrix}{\cos(\theta)} \\{\sin(\theta)}\end{bmatrix}}\left( {1 - {\cos\left( {{4\omega_{ex}t} + \phi + \overset{\hat{}}{\phi}} \right)}} \right)}} & (5)\end{matrix}$

This way, it is possible to obtain the two demodulated signals i_(αobs),i_(βobs) from the formulae (5) and (2) by applying a filtering, such as,for example, a low-pass filter, synonymous with the information on thereal position θ of the rotor 31 of the main machine 3:

$\begin{matrix}{\begin{bmatrix}i_{\alpha\;{obs}} \\i_{\beta\;{obs}}\end{bmatrix} = {{{H_{F}(s)}\left( {{2\begin{bmatrix}i_{\alpha h} \\i_{\beta h}\end{bmatrix}}{\sin\left( {{2\omega_{ex}t} + \hat{\phi}} \right)}} \right)} \approx {A\begin{bmatrix}{\cos(\theta)} \\{\sin(\theta)}\end{bmatrix}}}} & (6)\end{matrix}$

The two demodulated signals i_(αobs), i_(βobs) are therefore newrepresentations of the two filtered signals i_(αh); i_(βh) without theirhigh-frequency modulation.

A step of obtaining 14 of an estimated position {circumflex over (θ)} ofthe rotor 31 of the main machine 3 from the two demodulated signalsi_(αobs), i_(βobs) generated in the demodulation step 13. The obtainingstep 14 makes it possible to determine an estimated position from thetwo demodulated signals i_(αobs), i_(βobs), denoted {circumflex over(θ)} . As an example, the estimated position {circumflex over (θ)}estimated in the obtaining step 14 is made according to the followingmathematical expression:

$\begin{matrix}{\overset{\hat{}}{\theta} = {{atan}\left( \frac{i_{\beta\;{obs}}}{i_{\alpha\;{obs}}} \right)}} & (7)\end{matrix}$

After having estimated the estimated position {circumflex over (θ)} ofthe rotor 31 of the main machine 3, the estimation method 1 can alsocomprise a step of estimation of a speed {circumflex over ({dot over(θ)})} of the rotor 31 of the main machine 3, combined in the step ofobtaining 14 of the estimated position {circumflex over (θ)}. The speed{circumflex over ({dot over (θ)})} of the rotor 31 is the temporalderivative of the estimated position {circumflex over (θ)} of the rotor31.

According to another configuration, the estimated position {circumflexover (θ)} estimated in the obtaining step 14 can be produced using aphase-locked loop or an observer, for example an observer of Luenbergertype, for example taking account of the mechanical model of the machine.These algorithms minimise the estimation deviation between the estimatedposition {circumflex over (θ)}, in the preceding iteration step, and thereal position θ. This estimation deviation is obtained from thedemodulated signals i_(αobs), i_(βobs) and the estimated position{circumflex over (θ)} obtained at the preceding instant. Thesealgorithms can advantageously be used for the estimation of the speed{circumflex over ({dot over (θ)})} in addition to the obtaining of theestimated position {circumflex over (θ)} of the rotor 31.

In automatic mode, an observer or stator observer is an extension of amodel represented in state representation form, that is to say a dynamicsystem, via parameters called state variables. By definition, anobserver makes it possible to reconstruct the state of the modelobserved from the dynamic system and the measurements of otherquantities. This representation makes it possible to determine the stateof the system at any future instant by knowing the state at the initialinstant and the behaviour of the state variables. Thus, it is possibleto envisage using, instead of the mathematical expression (7), anobserver, and advantageously an observer of Luenberger type, in whichthe state variables include the position and the speed of the system.Advantageously, the model can consider the dynamics of the resistingtorque or of other mechanical parameters measured by or known to theuser. The method for estimating 1 the position of the rotor 31 is aniterative method, that is to say that the estimation method 1 can berepeated periodically. The four successive steps of measurement 11 ofthe current i_(abc), of determination and of isolation of harmonics 12,of demodulation 13 of the two filtered signals i_(αh); i_(βh) and ofobtaining 14 of the estimated position {circumflex over (θ)} cantherefore be iterated multiple times so as to refine the estimatedposition {circumflex over (θ)} and reduce any error between the realposition and the estimated position {circumflex over (θ)} of the rotor31 of the main machine 3.

FIG. 1B schematically represents the last two stages of the rotatingelectrical machine 2 composed of the main machine 3, the exciter 4coupled to the main machine 3 via a revolving three-phase rectifier 5and an estimation device 100 for operation when stopped or at low speed.The device for estimating the position of the rotor 31 of the mainmachine 3 is composed of four modules mirroring the four steps of theestimation method 1.

A measurement module 101, conditioning the measurement step 11, capableof measuring the current i_(abc) originating from the stator 32 of themain machine 3 and, possibly, capable of measuring the current i_(ex)originating from the stator 42 of the exciter 4. Also, the measurementmodule 101 also makes it possible to eliminate the measured noise at thesame time as the current i_(abc).

A module for determining and isolating harmonics 102 making it possibleto condition the step of determination and of isolation of harmonics 12presented previously. The module for determining and isolating harmonics102 generates two filtered signals i_(αh); i_(βh) from the noiselesscurrent i_(abc) obtained from the measurement module 101. Morespecifically, the module for determining and isolating harmonics 102makes it possible to transform current i_(abc) into the stationaryreference frame (α, β) by any transformation that makes it possible tomodel a three-phase system, such as, for example, a Clarketransformation or a Concordia transformation.

A module for demodulating 103 the two filtered signals i_(αh); i_(βh),making it possible to obtain two demodulated signals i_(αobs), i_(βobs),conditions the demodulation step 13. The module for demodulating 103 thetwo filtered signals i_(αh), i_(βh) is capable of collecting themeasurement of the current i_(ex) of the stator 42 of the exciter 4picked up by the measurement module 101 in order to generate the twodemodulated signals i_(αobs), i_(βobs) representing the information onthe real position 9 of the rotor 31 of the main machine 3.

The two demodulated signals i_(αobs), i_(βobs) are then recovered by amodule for obtaining 104 the estimated position {circumflex over (θ)} ofthe rotor 31 of the main machine 3. The obtaining module 104 conditionsthe step of obtaining 14 of the estimated position {circumflex over (θ)}of the rotor 31 of the main machine 3. Thus, the module for obtaining104 the estimated position {circumflex over (θ)} is configured todetermine, from the two demodulated signals i_(αobs), i_(βobs), theestimated position {circumflex over (θ)} of the rotor 31 according toseveral means.

Thus, by way of example, the estimated position {circumflex over (θ)} ofthe rotor 31 of the main machine 3 can be generated by the obtainingmodule 104 according to the mathematical expression (7):

$\begin{matrix}{\overset{\hat{}}{\theta} = {{atan}\left( \frac{i_{\beta\;{obs}}}{i_{\alpha\;{obs}}} \right)}} & (7)\end{matrix}$

Nevertheless, it is possible to envisage incorporating other algorithmsor procedures in the obtaining module 104 making it possible todetermine the estimated position {circumflex over (θ)}, such as, forexample, the use of a phase locking algorithm or of the observer (notrepresented) presented previously in FIG. 1A, for example of Luenbergertype taking into account the mechanical model of the machine.

Using these four steps comprising the step of measurement 11 of thecurrent i_(abc) conditioned by the measurement model 101, the step ofdetermination and of isolation of harmonics 12 conditioned by the modulefor determining and isolating harmonics 102, the step of demodulation 13of the two filtered signals i_(αh); i_(βh) conditioned by thedemodulation module 103 and the step of obtaining 14 of the estimatedposition {circumflex over (θ)} conditioned by the module for obtaining104 the estimated position {circumflex over (θ)}, it is possible todetermine the position of the rotor 31 of the main machine 3, and thespeed.

As a variant, the step of determination and of isolation of harmonics 12can include, in place of the step 12B of isolation of the two signals inquadrature i_(α); i_(β) an isolation step with anticipative, orfeedforward, action 12B′, represented in FIG. 1C, allowing the isolationof the two filtered signals i_(αh); i_(βh) while inducing a change offrequency of the harmonics of interest. The isolation step withfeedforward action 12B′ is preceded by a step 120′ allowing theprocessing of the current estimated speed {circumflex over ({dot over(θ)})} by the method. It should be noted that the estimated speed{circumflex over ({dot over (θ)})} corresponds to an estimation of theelectrical frequency of the machine denoted f_(e). In the case wherethis estimation of the speed {circumflex over ({dot over (θ)})} is notwithout noise, any means whose function is to eliminate high-frequencyvariations on the estimated speed {circumflex over ({dot over (θ)})} canbe taken into consideration in the step 120′. As an example, a low-passfiltering of the speed {circumflex over ({dot over (θ)})} making itpossible to obtain an estimated filtered speed, denoted {circumflex over(θ)}_(f), accompanied by an integrator in order to obtain the phase ofthe filtered speed {circumflex over (θ)}_(f), following the low-passfiltering, may be put in place in the step 120′:

{circumflex over (θ)}_(f)=∫{circumflex over ({dot over (θ)})}_(f)dt

The feedforward use of the speed {circumflex over ({dot over (θ)})}offers the advantage of ensuring a better conditioning of the signals inquadrature i_(α); i_(β) before the isolation thereof. Consequently, thefeedforward action in the step 12B′ allows a transformation of the twosignals in quadrature i_(α); i_(β) into filtered signals i_(αh); i_(βh)from the phase of the filtered speed {circumflex over (θ)}_(f). As anindicative example, this transformation is a Park transformation usingthe phase of the filtered speed {circumflex over (θ)}_(f) determined inthe step 120′. Unlike the Concordia transformation or the Clarketransformation, the Park transformation offers the benefit of allowing acentring of the frequency of the harmonics by eliminating the termlinked to the frequency f_(e) of the main machine 3 if it is consideredthat (f_(e)−{circumflex over ({dot over (θ)})}_(f))≈0. Thus, the twofiltered signals i_(αh); i_(βh) in the isolation step with feedforwardaction 12B′ form a pair of harmonics centred around the fundamentalmoment whose frequency, freed of the phase-shift linked to the frequencyf_(e) of the main machine 3, becomes:

⁻ ⁺n*f_(ex)

The phase of the filtered speed {circumflex over (θ)}_(f) obtained inthe step 120′ is then used in the step of obtaining 14 of the estimatedposition {circumflex over (θ)} in order to preserve the accuracy of theestimation which is then expressed, as an indicative example, accordingto the following formula:

{circumflex over (θ)}=f(i _(αobs) ,i _(βobs))+{circumflex over (θ)}_(f)

In which {circumflex over (θ)}_(f) represents the integration of thefiltered speed {circumflex over ({dot over (θ)})}_(f).

As a preferential example, the obtaining step 14 is performed accordingto the following mathematical expression:

$\overset{\hat{}}{\theta} = {{{atan}\left( \frac{i_{\beta\;{obs}}}{i_{\alpha\;{obs}}} \right)} + {\overset{\hat{}}{\theta}}_{f}}$

However, there may be some approximations, such as, for example, in thephase of the carrier of the rotor 31 of the main machine 3 or even forthe phase-shifting introduced in the filtering steps during thedemodulation 13 of the high-frequency signals.

Thus, other steps, illustrated in FIG. 2A can be added in order toeliminate the uncertainties cited.

FIG. 2A schematically represents the estimation method 1 in its mostcomprehensive version, that is to say the estimation method 1illustrated by FIG. 1A in which additional steps have been added. Thus,the estimation method 1, according to FIG. 2A, comprises the four stepsof measurement 11 of the current i_(abc), of determination and isolationof harmonics 12, of demodulation 13 of the two filtered signals i_(αh);i_(βh) and of obtaining 14 of the estimated position {circumflex over(θ)} adopting new configurations:

-   In place of the measurement of the current i_(ex) allowing the    reconstruction of the carrier, a direct estimation of a phase    {circumflex over (ϕ)} of the carrier by knowing the angular    frequency ω_(ex) of the exciter 4 can be envisaged. This phase    {circumflex over (ϕ)} of the carrier makes it possible to dispense    with the measurement of the current i_(ex) of the exciter 4 while    allowing a better knowledge of the phase of the carrier. In fact,    the estimation method 1 and the estimation device 100 are    preferentially associated with a rotating electrical machine with    three stages. However, through the use of the estimation of the    phase {circumflex over (ϕ)} of the carrier in place of the    measurement of the current i_(ex) of the exciter 4, the estimation    method 1 and the estimation device 100 can be associated with a    rotating electrical machine with a single stage or more than two    stages. In fact, in order to best predict the position of the rotor    31 of the main machine 3, the phase {circumflex over (ϕ)} of the    carrier must be known with accuracy. Thus, an additional step of    evaluation 16 of the phase {circumflex over (ϕ)} of the carrier can    be introduced into the estimation method 1. More specifically, the    demodulation step 13 is preceded by the step of evaluation 16 of the    phase {circumflex over (ϕ)} of the carrier. This step of evaluation    16 of the phase {circumflex over (ϕ)} of the carrier is illustrated    hereinbelow in FIG. 2C. This phase {circumflex over (ϕ)} of the    carrier is estimated from the angular frequency ω_(ex) of the    exciter 4, from the estimated position {circumflex over (θ)}    estimated in a preceding iteration of the estimation method 1 and    from the filtered signals i_(α) _(h) , i_(β) _(h) filtered in the    step of determination and of isolation of harmonics 12. The carrier    can be considered as a high-frequency harmonic obtained on the rotor    41 of the exciter 4.

Thus, the demodulation step 13 then receives as input the filteredsignals i_(α) _(h) , i_(β) _(h) more specifically containing theinformation on the position of the rotor 31 and the phase {circumflexover (ϕ)} of the carrier pre-estimated upstream. And, the demodulationstep 13 can dispense with the measurement of the current i_(ex) of theexciter 4.

-   In theory, the demodulation step 13 makes it possible to obtain two    ideal demodulated signals i_(αobs), i_(βobs), that is to say signals    completely refined and usable to determine the estimated position    {circumflex over (θ)} of the rotor 31 of the main machine 3.    However, experience tends to prove that the direct use of the    mathematical formula (7) making it possible to obtain the estimated    position {circumflex over (θ)} on the two demodulated signals    i_(αobs), i_(βobs) contains imperfections and can provoke    instability when the position obtained with the estimation method 1    is used in the control of the machine. In order to reduce the noise    following the demodulation step 13, a filtering step 17 can be put    in place. This filtering step 17 requires as input the two    demodulated signals i_(αobs), i_(βobs) and makes it possible to    reconstruct a sinusoidal form for the two demodulated signals    i_(αobs), i_(βobs). Thus, the filtering step 17 is positioned    between the demodulation step 13 and the step of obtaining 14 the    estimated position. The filtering step 17 makes it possible to    obtain pure demodulated signals i_(αobs), i_(αobs), that is to say    signals reconstructed from the two demodulated signals i_(αobs),    i_(βobs) stripped of all the undesirable effects such as, for    example, the noise induced by zero transition of the phase currents.    As an example, this filtering step 17 can be performed using an    adaptive bandpass filter taking into account electrical frequency    information of the machine, or it can advantageously be performed    using an extended Kalman filter considering their model with the    properties of the signals in quadrature. The Kalman filter can    advantageously be used also for the estimation of the speed.

With the disturbances eliminated, the mathematical formula (7) definedpreviously can be used on the new demodulated and filtered signalsi_(αobs), i_(βobs) refined in the step of obtaining 14 of the estimatedposition {circumflex over (θ)} of the rotor 31 of the main machine 3.Nevertheless, the method for estimating 1 the estimated position{circumflex over (θ)} introduce a series of phase-shifts on theestimated position {circumflex over (θ)} for each filter used. Forexample, any filtering applied following the demodulation step 13induces a phase shift which cannot be disregarded in the estimationmethod 1 because it is transferred automatically to the estimatedposition {circumflex over (θ)}. To be robust, the estimation method 1can comprise a step of correction 18 of the estimated position{circumflex over (θ)}. This correction step 18 is applied following thestep of obtaining 14 of the estimated position {circumflex over (θ)} ofthe rotor 31 of the main machine 3 in order to correct the induced phaseshift. The estimated position {circumflex over (θ)} is then corrected inthe correction step 18 with the following mathematical formula:

{circumflex over (θ)}_(corr)={circumflex over (θ)}+{circumflex over(ϕ)}_(corr)

In which {circumflex over (θ)}_(corr) is the corrected position of therotor 31 of the main machine 3 and {circumflex over (ϕ)}_(corr) is acorrection of the delays on the estimation of the position of the rotor31 making it possible to align the estimated position {circumflex over(θ)} with the real position of the rotor 31 of the main machine 3.

Furthermore, the correction of the delays {circumflex over (ϕ)}_(corr)is, in reality, a sum of several corrections considered:

-   A correction of the phase shifting of the filters used induced in    the demodulation 13, denoted {circumflex over (ϕ)}_(F)({circumflex    over (ω)}_(e)). In fact, the two demodulated signals i_(αobs),    i_(βobs) are generally delayed by the effect of the filtering. This    then affects the phase of the estimated position {circumflex over    (θ)} of the rotor 31 of the main machine 3. Thus, in order to    rectify that, this phase shift is calculated automatically and in    real time as a function of the speed {circumflex over ({dot over    (θ)})} of the main machine 3.

A correction of phase shift dependent on the electromagneticcharacteristics of the synchronous electrical machine {circumflex over(ϕ)}_(lc) induced by the phenomenon of electromagnetic saturation and/orof variation of the impedance of the stator circuit with temperature. Infact, each rotating electrical machine being defined by its ownarchitecture, it then comprises nonlinearity effects specific thereto.That makes it possible, for two rotating electrical machines having anidentical mode of operation, for the deviations between the realposition and the estimated position to be noted. The phase shiftcorrection dependent on the electromagnetic characteristics of thesynchronous electrical machine {circumflex over (ϕ)}_(lc) is thereforespecific to each rotating electrical machine provided with theestimation device 100 and/or the method for estimating 1 the position ofthe rotor 31 and is put in place empirically for example or then bysimulation and/or estimation when the estimation method 1 is put inplace. Thus, the correction of the delays {circumflex over (ϕ)}_(corr)can be defined as:

{circumflex over (ϕ)}_(corr)={circumflex over (ϕ)}_(F)({circumflex over(ω)}_(e))+{circumflex over (ϕ)}_(lc)

FIG. 2B represents the last two stages of the rotating electricalmachine 2 provided with the estimation device 100 described in FIG. 1Bin its most comprehensive version, that is to say comprising additionalmodules that make it possible to condition the comprehensive estimationmethod 1 described previously in FIG. 2A.

As indicated in FIG. 1B, the estimation device 100 comprises the modulefor measuring 101 the current i_(abc) originating from the stator 32 ofthe main machine 3, the module for determining and isolating harmonics102 of the two filtered signals i_(αh); i_(βh) from the current i_(abc),from the module for demodulating 103 the two filtered signals i_(αh);i_(βh) and from the module for obtaining 104 the estimated position{circumflex over (θ)} of the rotor 31.

Following the estimation of the estimated position {circumflex over (θ)}and of the speed {circumflex over ({dot over (θ)})} of the rotor 31, amodule for correcting 106 the estimated position {circumflex over (θ)}can be introduced. This correction module 106, which conditions the stepof correction 18 of the estimated position {circumflex over (θ)}, makesit possible to evaluate the corrected position {circumflex over(θ)}_(corr), which provides a more accurate estimation of the positionof the rotor 31 of the main machine 3.

The estimation device 100 also comprises a module for estimating 105 thephase {circumflex over (ϕ)} of the carrier. In order to estimate thephase {circumflex over (ϕ)}, the estimation module 105 requires thecorrected position {circumflex over (θ)}_(corr) from the precedingiteration and the two filtered signals i_(αh), i_(βh) and the angularfrequency ω_(ex) of the exciter 4. Through the use of these threeparameters, the estimation module 105 supplies the phase {circumflexover (ϕ)} of the carrier to the demodulation module 103. Nevertheless,it is possible to envisage replacing the estimated position {circumflexover (θ)} in place of the corrected position {circumflex over(θ)}_(corr) in the case of absence of a step of correction 18 of theestimated position {circumflex over (θ)}.

The demodulation module 103 then collects the phase {circumflex over(ϕ)} evaluated by the estimation module 105 and the two signals i_(α)_(h) ; i_(β) _(h) determined by the module for determining and isolatingharmonics 102, thus making it possible to dispense with the measurementof the current i_(ex) of the stator 42 of the exciter 4. Thus, themodule for demodulating 103 the two filtered signals i_(αh); i_(βh) alsomakes it possible to obtain the two demodulated signals i_(αobs),i_(βobs) from the carrier of angular frequency ω_(ex) of the exciter 4.

That allows an electrical machine comprising the exciter 4 and at leastone main machine 3 to be equipped with the estimation device 100 inorder to obtain the estimated position {circumflex over (θ)} or thecorrected position {circumflex over (θ)}_(corr).

FIG. 2C schematically represents the step of evaluation 16 of the phase{circumflex over (ϕ)} of the carrier in order to allow the demodulationstep 13 to be put in place.

In the state of the art, the evaluation of a phase {circumflex over (ϕ)}of a carrier is done generally using the current measured at the rotor31. However, this involves the use of an additional sensor in the rotor31, which is not possible in the context of a machine with multiplestages where the rotor current is not accessible.

In order to best evaluate the phase {circumflex over (ϕ)} of a carrierwithout measuring the excitation current at the stator 41 of the exciter4, the two filtered signals i_(αh), i_(βh), the angular frequency ω_(ex)of the control of the exciter 4 and the estimated position {circumflexover (θ)} of the rotor 31 of the main machine 3 are necessary.Advantageously, the estimated position {circumflex over (θ)} can bereplaced by the corrected position {circumflex over (θ)}_(corr) if thisposition is available in the estimation method 1.

As illustrated in FIG. 2C, before evaluating the phase {circumflex over(ϕ)}, a signal i_({circumflex over (d)}) _(h) is obtained by using theproperties of the Clarke or Concordia transform combining the estimatedposition {circumflex over (θ)} of the rotor 31 and the two filteredsignals i_(αh), i_(βh). The signal i_({circumflex over (d)}) _(h)obtained is an estimation of the high-frequency component aligned withthe flux of the rotor 31 of the main machine 3.

The signal i_({circumflex over (d)}) _(h) obtained is an image of thecarrier having the frequency and the phase of the signal induced on thestator 32 of the main machine 3. It is sufficient to determine the phaseof the signal at the frequency of interest, in a preferential case2ω_(ex), to obtain the phase {circumflex over (ϕ)}.

FIG. 3 represents the possible transformations of the current i_(abc) toa revolving reference frame or a stationary reference frame. Therevolving reference frame is defined by a first revolving axis d(direct) and a second revolving axis q (quadrature) centred at theintersection of the three-phase current i_(a), i_(b), i_(c). As the nameof the reference frame indicates, the first revolving axis d and thesecond revolving axis q undergo an angular variation linked to theposition θ used for the transformation. A transformation in a stationaryreference frame composed of a first fixed axis α and a second fixed axisβ is performed, as stated previously, using the Clarke transformation orthe Concordia transformation. By virtue of this conversion, the currenti_(abc) can be defined by a component on the first fixed axis α and byanother component on the second fixed axis β, that is to say the twosignals in quadrature i_(α); i_(β). Moreover, it is possible to envisageusing other types of transformation to a stationary reference frame.Consequently, another stationary reference frame could be obtained withother pairs of signals in quadrature.

Through this conversion, it is possible to obtain the spectrum of thecurrent i_(αβ) of the main machine 3 as represented in FIG. 4. Thespectrum of the current makes it possible to illustrate the mainharmonics of the signals in quadrature i_(α); i_(β).

As stated previously, the frequency of the main harmonics is acombination of the operating frequency f_(ex) of the exciter 4 or of oneof its multiples and of the frequency f_(e) of the main machine 3. Thus,the harmonics can have a frequency of the form f_(e−) ⁺2*f_(ex) or ofthe form f_(e−) ⁺4*f_(ex), or even of the form f_(e−) ⁺6*f_(ex).

1. A method for estimating the position of a rotor of a synchronous electrical machine without the injection of signals, comprising a rotor and a stator coupled to an inverted synchronous electrical machine, acting as exciter, via a rectifier, the rectifier being connected to the rotor excitation of the main machine, the estimation method comprising the following steps: a. measurement of a current i_(abc) circulating in the stator of the synchronous electrical machine; b. determination of two signals in quadrature i_(α); i_(β) according to a stationary reference frame from the current i_(abc) and isolation of two filtered signals i_(αh); i_(βh) from the two signals in quadrature i_(α); i_(β); c. demodulation of the two filtered signals i_(αh); i_(βh) in order to obtain two demodulated signals i_(αobs), i_(βobs), the step of demodulation of the two filtered signals i_(αh); i_(βh) using a measurement of a current i_(ex) of the stator of the inverted synchronous electrical machine; d. obtaining of an estimated position {circumflex over (θ)} of the rotor from the two demodulated signals i_(αobs), i_(βobs).
 2. The estimation method according to claim 1, wherein the estimated position {circumflex over (θ)} estimated in the step d is made according to the following mathematical expression: $\overset{\hat{}}{\theta} = {{atan}\left( \frac{i_{\beta\;{obs}}}{i_{\alpha\;{obs}}} \right)}$
 3. The estimation method according to claim 1, wherein the estimated position {circumflex over (θ)} estimated in the step d is done using an observer.
 4. The estimation method according to claim 1, wherein the two filtered signals i_(αh); i_(βh) have a frequency combining an operating frequency f_(ex) of the inverted synchronous electrical machine and a frequency f_(e) of the synchronous electrical machine according to the following formula: f_(e−) ⁺n*f_(ex) wherein n represents an even relative integer number.
 5. The estimation method according to claim 1, wherein the isolation of the two filtered signals i_(αh); i_(βh) from the two signals in quadrature i_(α); i_(β) is performed using a bandpass filter or a high-pass filter.
 6. The estimation method according to claim 1, comprising a step of filtering of the two demodulated signals i_(αobs), i_(βobs) between the step c and the step d, the filtering step being performed using a bandpass filter or an extended Kalman filter.
 7. The estimation method according to claim 2, comprising a step of estimation of the speed {circumflex over ({dot over (θ)})} of the rotor of the synchronous electrical machine from the estimated position {circumflex over (θ)} of the rotor of the synchronous electrical machine.
 8. The estimation method according to claim 7, comprising a step of isolation with anticipative action of the two filtered signals i_(αh); i_(βh) from the two signals in quadrature i_(α); i_(β) and a phase of a filtered speed {circumflex over ({dot over (θ)})}_(f) of the rotor, the filtered speed {circumflex over ({dot over (θ)})}_(f) of the rotor representing the speed {circumflex over ({dot over (θ)})} of the rotor when filtered.
 9. The estimation method according to claim 1, comprising a step of correction of the estimated position {circumflex over (θ)} with the following mathematical formula: {circumflex over (θ)}_(corr)={circumflex over (θ)}+{circumflex over (ϕ)}_(corr) wherein {circumflex over (ϕ)}_(corr) is a correction of the delays on the estimation of the position and {circumflex over (θ)}_(corr) is a corrected position of the rotor of the synchronous electrical machine.
 10. The estimation method according to claim 9, wherein the correction of the delays {circumflex over (θ)}_(corr) is the sum of a phase-shift correction of the filters used {circumflex over (ϕ)}_(F) in the estimation method and of a phase-shift correction dependent on the electromagnetic characteristics of the synchronous electrical machine {circumflex over (ϕ)}_(LC).
 11. The estimation method according to claim 1, the estimation method being able to be repeated periodically, wherein the demodulation step is preceded by a step of evaluation of a phase {circumflex over (ϕ)} of a carrier from the filtered signals i_(α) _(h) ; i_(β) _(h) , of an angular frequency ω_(ex) of the inverted synchronous electrical machine and of the estimated position {circumflex over (θ)} in a preceding iteration of the estimation method, the carrier being obtained at the rotor of the inverted synchronous electrical machine.
 12. A device for estimating the position of a rotor of a synchronous electrical machine coupled to an inverted synchronous electrical machine via a rectifier for operation when stopped or at low speed according to one of the preceding claims, comprising: a) a module for measuring a current i_(abc) circulating in the stator of the synchronous electrical machine; b) a module for determining and isolating harmonics of two filtered signals i_(αh); i_(βh) from the current i_(abc); c) a module for demodulating the two filtered signals i_(αh); i_(βh) from a measurement of the current i_(ex) of the stator of the inverted synchronous electrical machine or of a carrier of angular frequency ω_(ex) of the inverted synchronous electrical machine in order to obtain two demodulated signals i_(αobs), i_(βobs); d) an obtaining module configured to determine an estimated position {circumflex over (θ)} of the rotor of the synchronous electrical machine from the two demodulated signals i_(αobs), i_(βobs).
 13. An electrical machine comprising an inverted electrical machine and at least one synchronous electrical machine equipped with the estimation device according to claim
 12. 